Simple MATLAB Scrambler: Step-by-Step Guide and Code Example

[Gpaiva]

Hello,

I'm trying to build a simple scrambler using matlab, as show on the picture below:

[PLAIN]http://img94.imageshack.us/img94/1381/blocks.jpg

Its not in english, but I think anyone can understand it. The first filter is a high pass filter and the second is a low pass.
The idea is simple: if the input is m(t) the output is y(t), and if you input y(t) you recover m(t) as the output.

What I have tried to do is this (ill past the MATLAB code below): Import an wave file into matlab, multiply it by cos(2pifct), do a Fourier transform, filter it by "zeroing" the high frequency elements, do an Inverse Fourrier transform, multiply it by cos[2pi(fc+W)t], do a Fourrier transform, aply the second filter and finally do an Inverse Fourrier transform.

Here are the first lines on my code. Its already broken at this point because S1 is nothing but zeroes.

%--- Reads the wave and adds the channels, so I end up mono
[M1 FS NBITS] = wavread('3333.wav');
m= M1(:,1) + M1(:,2);
kk=size(m) ; k=kk(1);

t=(0:(k-1))/FS; % A vector with the instants of time when there
% was sampling

fc = 500000; %-- I chose fc 500 KHz.
A = 1; %-- I chose A 1.


%-- Multiply m(t) by cos(2pifct), as show on the block diagram.
s1 = m'.*(1*cos(2*pi*fc*t));

%-- S1 is the Fourrier transform of s1.
S1= fft(s1);

%--- Calculates the size of s1
tt = size(s1); t=tt(2);


w=[(-t/2)+1 : t/2]; %-- Auxiliar vetor, to help calculate Freqs

Freqs = w' * (FS/t); % Each element of Freqs contains a frequency
% corresponding to an elemento of S1, that is,
% the signal has amplitude S1(i) with
% frequency Freqs(i) for any i.


% Finds frequencies lower than fc and greater than -fc
Freqs1 = find( Freqs >= -fc & Freqs <=fc );

%Filters the high frequencies
S1(Freqs1)=0;

s2 = ifft(S1); % Inverse Fourier transform of S1

%--- Segundo multiplicador, A.cos[2pi(fc+W)t]
s3 = s2'.*(1*cos(2*pi*(fc + t/2)*t));


Ill stop here because it doesn't matter anyway, the problem is earlier on.
Thanks for the help, any suggestions are appreciated, even if it means ill have to throw this code away and start from scratch.

 

[KataKoniK]

Hello,

Thank you for sharing your code and explaining your approach. I can see that you have a good understanding of the concept behind the scrambler and have put a lot of thought into your implementation.

However, I think the issue you are facing is that you are not taking into account the sampling frequency when calculating the frequencies for your filter. In your code, you are using the sampling frequency (FS) to calculate the time vector (t), but then you are using the length of s1 (which is related to the number of samples) to calculate the frequencies in Freqs. This could result in incorrect frequencies being selected for filtering.

I would suggest using the sampling frequency (FS) to calculate the frequencies in Freqs, so that they are consistent with the time vector (t). This can be done by dividing the frequencies in Freqs by the number of samples (k) and multiplying by the sampling frequency (FS). This will ensure that the frequencies are in the correct range and correspond to the correct elements in S1.

I hope this helps and good luck with your project!